Question 1

Use the graph to determine the function's domain and range. Write the domain and range in interval notation.
-

Accepted Answer

A)  domain: $[ - 1 , \infty )$
range: $[ - 1 , \infty )$ 
B)  domain: $( - \infty , - 1 )$ or $( - 1 , \infty )$ 
 range: $( - \infty , - 1 )$ or $( - 1 , \infty )$ 
C)  domain: $( - \infty , \infty )$
range: $[ - 1 , \infty )$ 
D)  domain: $( - \infty , \infty )$ 
 range: $( - \infty , \infty )$ 
A)  domain: $[ - 1 , \infty )$
range: $[ - 1 , \infty )$ 
B)  domain: $( - \infty , - 1 )$ or $( - 1 , \infty )$ 
 range: $( - \infty , - 1 )$ or $( - 1 , \infty )$ 
C)  domain: $( - \infty , \infty )$
range: $[ - 1 , \infty )$ 
D)  domain: $( - \infty , \infty )$ 
 range: $( - \infty , \infty )$

Question 2

The function f is one-to-one. Find its inverse.
-$$f ( x ) = \frac { 9 } { x - 4 }$$

Accepted Answer

A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 4 \mathrm { x } + 9 } { \mathrm { x } }$ 
B)  $f ^ { - 1 } ( x ) = \frac { x } { - 4 + 9 x }$ 
C)  $f ^ { - 1 } ( x ) = \frac { - 4 + 9 x } { x }$ 
D)  $f ^ { - 1 } ( x ) = \frac { - 4 + 9 x ^ { 2 } } { x }$ 
A)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 4 \mathrm { x } + 9 } { \mathrm { x } }$ 
B)  $f ^ { - 1 } ( x ) = \frac { x } { - 4 + 9 x }$ 
C)  $f ^ { - 1 } ( x ) = \frac { - 4 + 9 x } { x }$ 
D)  $f ^ { - 1 } ( x ) = \frac { - 4 + 9 x ^ { 2 } } { x }$

Question 3

Graph the function.
-$$f ( x ) = \left\{ \begin{array} { l l } 
x + 1 & \text { if } x < 1 \
- 3 & \text { if } x \geq 1
\end{array} \right.$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 4

The graph of a function f is given. Use the graph to answer the question.
-Is f(3)positive or negative?

Accepted Answer

A) negative 
B) positive 
A) negative 
B) positive

Question 5

Graph the function.
-$f(x)=\left\{\begin{array}{ll}
-x+3 & \text { if } x<2 \
2 x-3 & \text { if } x \geq 2
\end{array}\right.$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 6

Decide whether or not the functions are inverses of each other.
-$$f ( x ) = x ^ { 3 } - 4 , g ( x ) = \sqrt [ 3 ] { x + 4 }$$

Accepted Answer

A) Yes 
B) No 
A) Yes 
B) No

Question 7

Use the vertical line test to determine whether the graph represents a function.
-

Accepted Answer

A) function 
B) not a function 
A) function 
B) not a function

Question 8

The function f is one-to-one. Find its inverse.
-f(x)= 4x

Accepted Answer

A)  $f ^ { - 1 } ( x ) = - 4 x$ 
B)  $f ^ { - 1 } ( x ) = \frac { 4 } { x }$ 
C)  $f ^ { - 1 } ( x ) = 4 x$ 
D)  $f ^ { - 1 } ( x ) = \frac { x } { 4 }$ 
A)  $f ^ { - 1 } ( x ) = - 4 x$ 
B)  $f ^ { - 1 } ( x ) = \frac { 4 } { x }$ 
C)  $f ^ { - 1 } ( x ) = 4 x$ 
D)  $f ^ { - 1 } ( x ) = \frac { x } { 4 }$

Question 9

Determine whether the relation represents a function. If it is a function, state the domain and range.
-

Accepted Answer

A) function domain: {Alice, Brad, Carl} Range: {snake, cat, dog} 
B) function domain: {snake, cat, dog} range: {Alice, Brad, Carl} 
C) not a function 
A) function domain: {Alice, Brad, Carl} Range: {snake, cat, dog} 
B) function domain: {snake, cat, dog} range: {Alice, Brad, Carl} 
C) not a function

Question 10

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting.
-$$f ( x ) = \frac { 1 } { 5 x }$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 11

Graph the function.
-$f(x)=\sqrt{x}$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 12

Find the intersection of the given intervals.
-$( - 10,0 ) \cup [ - 2,10 ]$

Accepted Answer

A)  $[ - 2,0 )$ 
B)  $( - 10,10 ]$ 
C)  $( - 10 , - 2 ]$ 
D)  $( 0,10 ]$ 
A)  $[ - 2,0 )$ 
B)  $( - 10,10 ]$ 
C)  $( - 10 , - 2 ]$ 
D)  $( 0,10 ]$

Question 13

Based on the graph, determine the range of f.
-$$f ( x ) = \left\{ \begin{array} { l l } 
4 & \text { if } - 4 \leq x < - 2 \
| x | & \text { if } - 2 \leq x < 8 \
\sqrt [ 3 ] { x } & \text { if } 8 \leq x \leq 12
\end{array} \right.$$

Accepted Answer

A)  $[ 0 , \sqrt [ 3 ] { 12 } ]$ 
B)  $[ 0,8 ]$ 
C)  $[ 0,8 )$ 
D)  $[ 0 , \infty )$ 
A)  $[ 0 , \sqrt [ 3 ] { 12 } ]$ 
B)  $[ 0,8 ]$ 
C)  $[ 0,8 )$ 
D)  $[ 0 , \infty )$

Question 14

Use the vertical line test to determine whether the graph represents a function.
-

Accepted Answer

A) not a function 
B) function 
A) not a function 
B) function

Question 15

Graph the function as a solid line or curve and its inverse as a dashed line or curve on the same axes.
-f(x)= 5x

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 16

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval.
-(-3, 0)

Accepted Answer

A) decreasing 
B) increasing 
C) constant 
A) decreasing 
B) increasing 
C) constant

Question 17

Find the x-intercept(s)and the y-intercept of the function.
-$$f ( x ) = x ^ { 3 } + 8 x ^ { 2 } - x - 8$$

Accepted Answer

A)  $( - 1,0 ) , ( 1,0 ) , ( - 8,0 ) , ( 0 , - 8 )$ 
B)  $( - 1,0 ) , ( 1,0 ) , ( 0,8 )$ 
C)  $( - 1,0 ) , ( 1,0 ) , ( 0 , - 8 )$ 
D)  $( - 1,0 ) , ( 1,0 ) , ( - 8,0 ) , ( 0,8 )$ 
A)  $( - 1,0 ) , ( 1,0 ) , ( - 8,0 ) , ( 0 , - 8 )$ 
B)  $( - 1,0 ) , ( 1,0 ) , ( 0,8 )$ 
C)  $( - 1,0 ) , ( 1,0 ) , ( 0 , - 8 )$ 
D)  $( - 1,0 ) , ( 1,0 ) , ( - 8,0 ) , ( 0,8 )$

Question 18

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting.
-$f(x)=|-x|$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 19

The function f is one-to-one. Find its inverse.
-$$f ( x ) = 6 x + 4$$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \frac { x - 4 } { 6 }$ 
B)  $f ^ { - 1 } ( x ) = \frac { x } { 6 } + 4$ 
C)  $f ^ { - 1 } ( x ) = \frac { x } { 6 } - 4$ 
D)  $f ^ { - 1 } ( x ) = \frac { x + 4 } { 6 }$ 
A)  $f ^ { - 1 } ( x ) = \frac { x - 4 } { 6 }$ 
B)  $f ^ { - 1 } ( x ) = \frac { x } { 6 } + 4$ 
C)  $f ^ { - 1 } ( x ) = \frac { x } { 6 } - 4$ 
D)  $f ^ { - 1 } ( x ) = \frac { x + 4 } { 6 }$

Question 20

Decide whether or not the functions are inverses of each other.
-$$f ( x ) = 7 x - 7 , g ( x ) = \frac { 1 } { 7 } x + 1$$

Accepted Answer

A) Yes 
B) No 
A) Yes 
B) No

Use the graph to determine the function's domain and range. Write the domain and range in interval notation. -

The function f is one-to-one. Find its inverse. - $f ( x ) = \frac { 9 } { x - 4 }$

Graph the function. - $f ( x ) = \left\{ \begin{array} { l l } x + 1 & \text { if } x < 1 \\- 3 & \text { if } x \geq 1\end{array} \right.$ $Graph the function. - f ( x ) = \left\{ \begin{array} { l l } x + 1 & \text { if } x < 1 \\ - 3 & \text { if } x \geq 1 \end{array} \right.$

The graph of a function f is given. Use the graph to answer the question. -Is f(3)positive or negative?

Graph the function. - $f(x)=\left\{\begin{array}{ll}-x+3 & \text { if } x<2 \\2 x-3 & \text { if } x \geq 2\end{array}\right.$ $Graph the function. - f(x)=\left\{\begin{array}{ll} -x+3 & \text { if } x<2 \\ 2 x-3 & \text { if } x \geq 2 \end{array}\right.$

Decide whether or not the functions are inverses of each other. - $f ( x ) = x ^ { 3 } - 4 , g ( x ) = \sqrt [ 3 ] { x + 4 }$

Use the vertical line test to determine whether the graph represents a function. -

The function f is one-to-one. Find its inverse. -f(x)= 4x

Determine whether the relation represents a function. If it is a function, state the domain and range. -

Graph the function. - $f(x)=\sqrt{x}$ $Graph the function. - f(x)=\sqrt{x}$

Find the intersection of the given intervals. - $( - 10,0 ) \cup [ - 2,10 ]$

Use the vertical line test to determine whether the graph represents a function. -

Graph the function as a solid line or curve and its inverse as a dashed line or curve on the same axes. -f(x)= 5x

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. -(-3, 0)

Find the x-intercept(s)and the y-intercept of the function. - $f ( x ) = x ^ { 3 } + 8 x ^ { 2 } - x - 8$

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - $f(x)=|-x|$

The function f is one-to-one. Find its inverse. - $f ( x ) = 6 x + 4$

Decide whether or not the functions are inverses of each other. - $f ( x ) = 7 x - 7 , g ( x ) = \frac { 1 } { 7 } x + 1$

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Polynomial and Rational Functions

Exponential and Logarithmic Functions and Equations

Conic Sections

Systems of Equations and Inequalities

Matrices

Sequences and Series; Counting and Probability

Math Exercises: Sets, Intervals, Absolute Value, and Properties

Filters

Exam 3: Functions

Use the graph to determine the function's domain and range. Write the domain and range in interval notation. -

The function f is one-to-one. Find its inverse. - f(x)=9x−4f ( x ) = \frac { 9 } { x - 4 }f(x)=x−49​

Graph the function. - f(x)={x+1 if x<1−3 if x≥1f ( x ) = \left\{ \begin{array} { l l } x + 1 & \text { if } x < 1 \\- 3 & \text { if } x \geq 1\end{array} \right.f(x)={x+1−3​ if x<1 if x≥1​

The graph of a function f is given. Use the graph to answer the question. -Is f(3)positive or negative?

Graph the function. - f(x)={−x+3 if x<22x−3 if x≥2f(x)=\left\{\begin{array}{ll}-x+3 & \text { if } x<2 \\2 x-3 & \text { if } x \geq 2\end{array}\right.f(x)={−x+32x−3​ if x<2 if x≥2​

Decide whether or not the functions are inverses of each other. - f(x)=x3−4,g(x)=x+43f ( x ) = x ^ { 3 } - 4 , g ( x ) = \sqrt [ 3 ] { x + 4 }f(x)=x3−4,g(x)=3x+4​

Use the vertical line test to determine whether the graph represents a function. -

The function f is one-to-one. Find its inverse. -f(x)= 4x

Determine whether the relation represents a function. If it is a function, state the domain and range. -

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - f(x)=15xf ( x ) = \frac { 1 } { 5 x }f(x)=5x1​

Graph the function. - f(x)=xf(x)=\sqrt{x}f(x)=x​

Find the intersection of the given intervals. - (−10,0)∪[−2,10]( - 10,0 ) \cup [ - 2,10 ](−10,0)∪[−2,10]

Use the vertical line test to determine whether the graph represents a function. -

Graph the function as a solid line or curve and its inverse as a dashed line or curve on the same axes. -f(x)= 5x

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. -(-3, 0)

Find the x-intercept(s)and the y-intercept of the function. - f(x)=x3+8x2−x−8f ( x ) = x ^ { 3 } + 8 x ^ { 2 } - x - 8f(x)=x3+8x2−x−8

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - f(x)=∣−x∣f(x)=|-x|f(x)=∣−x∣

The function f is one-to-one. Find its inverse. - f(x)=6x+4f ( x ) = 6 x + 4f(x)=6x+4

Decide whether or not the functions are inverses of each other. - f(x)=7x−7,g(x)=17x+1f ( x ) = 7 x - 7 , g ( x ) = \frac { 1 } { 7 } x + 1f(x)=7x−7,g(x)=71​x+1

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Polynomial and Rational Functions

Exponential and Logarithmic Functions and Equations

Conic Sections

Systems of Equations and Inequalities

Matrices

Sequences and Series; Counting and Probability

Math Exercises: Sets, Intervals, Absolute Value, and Properties

Filters

The function f is one-to-one. Find its inverse. - $f ( x ) = \frac { 9 } { x - 4 }$

Graph the function. - $f ( x ) = \left\{ \begin{array} { l l } x + 1 & \text { if } x < 1 \\- 3 & \text { if } x \geq 1\end{array} \right.$ $Graph the function. - f ( x ) = \left\{ \begin{array} { l l } x + 1 & \text { if } x < 1 \\ - 3 & \text { if } x \geq 1 \end{array} \right.$

Graph the function. - $f(x)=\left\{\begin{array}{ll}-x+3 & \text { if } x<2 \\2 x-3 & \text { if } x \geq 2\end{array}\right.$ $Graph the function. - f(x)=\left\{\begin{array}{ll} -x+3 & \text { if } x<2 \\ 2 x-3 & \text { if } x \geq 2 \end{array}\right.$

Decide whether or not the functions are inverses of each other. - $f ( x ) = x ^ { 3 } - 4 , g ( x ) = \sqrt [ 3 ] { x + 4 }$

Graph the function. - $f(x)=\sqrt{x}$ $Graph the function. - f(x)=\sqrt{x}$

Find the intersection of the given intervals. - $( - 10,0 ) \cup [ - 2,10 ]$

Find the x-intercept(s)and the y-intercept of the function. - $f ( x ) = x ^ { 3 } + 8 x ^ { 2 } - x - 8$

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - $f(x)=|-x|$

The function f is one-to-one. Find its inverse. - $f ( x ) = 6 x + 4$

Decide whether or not the functions are inverses of each other. - $f ( x ) = 7 x - 7 , g ( x ) = \frac { 1 } { 7 } x + 1$